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On Edge-Disjoint Spanning Trees in a Randomly Weighted Complete Graph

Part of: Graph theory

Published online by Cambridge University Press:  09 October 2017

ALAN FRIEZE  and
TONY JOHANSSON
ALAN FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: alan@random.math.cmu.edu)
TONY JOHANSSON
Affiliation:
Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden (e-mail: tony.johanssson@math.uu.se)
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Abstract

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Assume that the edges of the complete graph Kn are given independent uniform [0, 1] weights. We consider the expected minimum total weight μk of k ⩽ 2 edge-disjoint spanning trees. When k is large we show that μk ≈ k 2. Most of the paper is concerned with the case k = 2. We show that m 2 tends to an explicitly defined constant and that μ 2 ≈ 4.1704288. . . .

MSC classification

Primary: 05C80: Random graphs
Secondary: 05C22: Signed and weighted graphs

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 2 , March 2018 , pp. 228 - 244
Copyright
Copyright © Cambridge University Press 2017 

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